I have been contacted by a debt collection agency and the amount they say I owe is much higher than what is on a credit report I recently received. What amount is right/should I pay?

If this is an old debt you try to negotiate a settlement. I would not trust the amount on a credit report, but the amount listed by the collector has fees and interest added to it that you may be able to negotiate down.

The credit report is just that a report and is often not exact.

You owe what amount you are legally obligated to owe. You should be aware of that sum since you borrowed it.
You may ask the lender to provide you with a detailed list of all debt to prove the amount owed if you are not sure.

Often the report may merely show the amount before late fees, before interest and other charges.